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Why Long-Dated Euro Swap Rates Can Fall Below Shorter Tenors

Article Quant Q&A · Author: David Duarte
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Summary

The document discusses a quoted 50-year euro swap rate of -0.58% and asks how to interpret the unusually shaped long end of the swap curve. The question notes positive carry for paying fixed and suggests limited liquidity may be influencing long-tenor pricing. The responses point to convexity as one reason long-dated swap rates can sit below rates at shorter maturities: a receiver position in the longer tenor paired with a payer position in the shorter tenor could otherwise capture convexity value, which the curve may price in through lower long-end rates.

A second response provides historical context, saying the 2-year to 50-year spread had been near that level in 2008, when the European Central Bank raised rates contrary to market expectations. The exchange is brief and offers no quantitative derivation, trade construction, or liquidity analysis, so it gives context rather than a complete valuation framework.

Key ideas

  • Convexity can help explain why very long swap rates are lower than rates at shorter maturities.
  • A receiver position in a long tenor paired with a payer position in a shorter tenor may have convexity value.
  • Long-tenor illiquidity is raised as a possible influence on the euro swap curve.
  • The exchange compares the curve shape with conditions around the ECB's unexpected 2008 rate hike.

Tags

Fixed incomeDerivatives pricingCarry
Full text
# What do you think of 50y swap at -0.58%?


# What do you think of 50y swap at -0.58%?












To start an exchange of ideas, what do you think of the 50y eur swap at -0.58%?

At this moment, the carry for paying 50y fixed is positive and the low liquidity of long tenors is shaping the curve in a way we have never seen before. This is the shape of the eur swap curve today.

## Answer by dm63 (score 4)

https://quant.stackexchange.com/a/51600

The long end of swap curves are often inverted due to convexity. For example, if 30s/50s were flat , there would be ‘free’ convexity to be had by receiving 50s and paying 30s. Hence, 50yr swap rates are lower than 30yr rates to offset the value of this convexity.

## Answer by David Duarte (score 2)

https://quant.stackexchange.com/a/51607

To add a bit more color, the 2s50s were only close to this level in 2008 when the ECB hiked against all market expectations

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.